Structural Addenda to the Reflexive Spiral Framework

This document is an integral extension of the main reflexive‑spiral thesis and is uploaded separately due to its scope and foundational importance. It consolidates and expands the structural backbone of the framework by presenting a unified account of how the asymmetry parameter \kappa , the finite recursion depth N_{\mathrm{trunc}}, and the Postnikov–Gödel tower jointly determine the vacuum‑energy scale, black‑hole information dynamics, holographic leakage, and the emergence of topological dark‑matter knots. Addenda A–E establish the quantitative core: the modified gravitational action, the suppression relation \rho _{\mathrm{vac}}\sim \kappa ^2/N_{\mathrm{trunc}}^{\, p}, the geometric meaning of the exponent p, the origin and universality of \kappa , and the necessity of a finite recursion tower with N_{\mathrm{trunc}}\approx 120\mathrm{–}130. Addenda F–H develop the dynamical and phenomenological consequences, including the recursion‑limited Page curve, early information recovery, gravitational‑wave echoes, holographic leakage, and the formation of stable topological defects behaving as dark matter. Together, these components show that dark energy, black‑hole unitarity, scalar‑sector dynamics, and dark‑matter phenomenology arise from a single geometric principle: a self‑referential universe that cannot complete its own tower and therefore leaves behind a structured residue of curvature, memory, and topological obstruction. This addendum provides a self‑contained but essential component of the overall thesis, clarifying the global coherence and inevitability of the framework.